Abstract

Dielectric transmission gratings with a similar period as the wavelength of the incident light can exhibit strong polarization dependence. By optimizing the groove width of a negative first-order Littrow transmission grating it can be achieved that light is transmitted to the zeroth order for one polarization, regardless of the groove depth, while it is efficiently diffracted for the other polarization. An investigation of this remarkable effect, based on a modal field representation inside the grating, as well as experimental results are presented.

© 2007 Optical Society of America

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  1. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
    [CrossRef]
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    [CrossRef]
  3. K. Yokomori, "Dielectric surface-relief gratings with high diffraction efficiencies," Appl. Opt. 23, 2303-2310 (1984).
    [CrossRef] [PubMed]
  4. D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, "Production of in-fiber gratings using a diffractive optical element," Electron. Lett. 29, 566-568 (1993).
    [CrossRef]
  5. D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
    [CrossRef]
  6. D. Strickland and G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56, 219-221 (1985).
    [CrossRef]
  7. A. Liem, J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, and A. Tünnermann, "High average power femtosecond fiber CPA system," in Advanced Solid-State Lasers, M.E.Fermann and L.R.Marshall, eds., Vol. 68 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 128-132.
  8. J. Limpert, T. Schreiber, T. Clausnitzer, K. Zöllner, H.-J. Fuchs, E.-B. Kley, H. Zellmer, and A. Tünnermann, "High-power femtosecond Yb-doped fiber amplifier," Opt. Express 10, 628-638 (2002).
    [PubMed]
  9. H. T. Nguyen, B. W. Shore, S. J. Bryan, J. A. Britten, R. D. Boyd, and M. D. Perry, "High-efficiency fused-silica transmission gratings," Opt. Lett. 22, 142-144 (1997).
    [CrossRef] [PubMed]
  10. T. Clausnitzer, J. Limpert, K. Zöllner, H. Zellmer, H.-J. Fuchs, E.-B. Kley, A. Tünnermann, M. Jupé, and D. Ristau, "Highly-efficient transmission gratings in fused silica for chirped pulse amplification systems," Appl. Opt. 42, 6934-6938 (2003).
    [CrossRef] [PubMed]
  11. T. Clausnitzer, E.-B. Kley, H.-J. Fuchs, and A. Tünnermann, "Highly efficient polarization independent transmission gratings for pulse stretching and compression," in Optical Fabrication, Testing and Metrology, R. Geyl, D. Rimmer, and L. Wang, eds., Proc. SPIE 5252, 174-182 (2003).
    [CrossRef]
  12. A. Drauschke, "Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization," J. Opt. A 8, 511-517 (2006).
    [CrossRef]
  13. J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P.Herzig ed. (Taylor & Francis, 1997), pp. 31-52.
  14. R. C. Enger and S. K. Case, "Optical elements with ultrahigh spatial-frequency surface corrugations," Appl. Opt. 22, 3220-3228 (1983).
    [CrossRef] [PubMed]
  15. M. Schmitz, R. Bräuer, and O. Bryngdahl, "Gratings in the resonance domain as polarizing beam splitters," Opt. Lett. 20, 1830-1831 (1995).
    [CrossRef] [PubMed]
  16. P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
    [CrossRef]
  17. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, and O. Parriaux, "An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings," Opt. Express 13, 10448-10456 (2005).
    [CrossRef] [PubMed]
  18. R. E. Collin, "Reflection and transmission at a slotted dielectric interface," Can. J. Phys. 34, 398-411 (1956).
    [CrossRef]
  19. S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).
  20. A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Electron. 37, 309-330 (2005).
    [CrossRef]

2006 (1)

A. Drauschke, "Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization," J. Opt. A 8, 511-517 (2006).
[CrossRef]

2005 (2)

2003 (2)

T. Clausnitzer, J. Limpert, K. Zöllner, H. Zellmer, H.-J. Fuchs, E.-B. Kley, A. Tünnermann, M. Jupé, and D. Ristau, "Highly-efficient transmission gratings in fused silica for chirped pulse amplification systems," Appl. Opt. 42, 6934-6938 (2003).
[CrossRef] [PubMed]

T. Clausnitzer, E.-B. Kley, H.-J. Fuchs, and A. Tünnermann, "Highly efficient polarization independent transmission gratings for pulse stretching and compression," in Optical Fabrication, Testing and Metrology, R. Geyl, D. Rimmer, and L. Wang, eds., Proc. SPIE 5252, 174-182 (2003).
[CrossRef]

2002 (1)

1999 (1)

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
[CrossRef]

1997 (1)

1995 (1)

1993 (1)

D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, "Production of in-fiber gratings using a diffractive optical element," Electron. Lett. 29, 566-568 (1993).
[CrossRef]

1992 (1)

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

1985 (1)

D. Strickland and G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56, 219-221 (1985).
[CrossRef]

1984 (1)

1983 (1)

1982 (1)

1981 (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
[CrossRef]

1956 (2)

R. E. Collin, "Reflection and transmission at a slotted dielectric interface," Can. J. Phys. 34, 398-411 (1956).
[CrossRef]

S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).

Adams, J. L.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
[CrossRef]

Anderson, D. Z.

D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, "Production of in-fiber gratings using a diffractive optical element," Electron. Lett. 29, 566-568 (1993).
[CrossRef]

Andrewartha, J. R.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
[CrossRef]

Botten, L. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
[CrossRef]

Boyd, R. D.

Bräuer, R.

Britten, J. A.

Bryan, S. J.

Bryngdahl, O.

Cambril, E.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
[CrossRef]

Case, S. K.

Chavel, P.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
[CrossRef]

Clausnitzer, T.

Collin, R. E.

R. E. Collin, "Reflection and transmission at a slotted dielectric interface," Can. J. Phys. 34, 398-411 (1956).
[CrossRef]

Craig, M. S.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
[CrossRef]

Drauschke, A.

A. Drauschke, "Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization," J. Opt. A 8, 511-517 (2006).
[CrossRef]

Enger, R. C.

Erdogan, T.

D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, "Production of in-fiber gratings using a diffractive optical element," Electron. Lett. 29, 566-568 (1993).
[CrossRef]

Fuchs, H.-J.

Gaylord, T. K.

Gnall, R. P.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

Hazart, J.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
[CrossRef]

Jupé, M.

Kämpfe, T.

Kley, E.-B.

Koch, T. L.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

Lalanne, P.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
[CrossRef]

Launois, H.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
[CrossRef]

Liem, A.

A. Liem, J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, and A. Tünnermann, "High average power femtosecond fiber CPA system," in Advanced Solid-State Lasers, M.E.Fermann and L.R.Marshall, eds., Vol. 68 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 128-132.

Limpert, J.

McPhedran, R. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
[CrossRef]

Mizrahi, V.

D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, "Production of in-fiber gratings using a diffractive optical element," Electron. Lett. 29, 566-568 (1993).
[CrossRef]

Moharam, M. G.

Mourou, G.

D. Strickland and G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56, 219-221 (1985).
[CrossRef]

Mulgrew, P. P.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

Nguyen, H. T.

Nolte, S.

A. Liem, J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, and A. Tünnermann, "High average power femtosecond fiber CPA system," in Advanced Solid-State Lasers, M.E.Fermann and L.R.Marshall, eds., Vol. 68 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 128-132.

Ostermeyer, F.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

Parriaux, O.

Perry, M. D.

Peschel, U.

Ristau, D.

Rytov, S. M.

S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).

Schmitz, M.

Schreiber, T.

J. Limpert, T. Schreiber, T. Clausnitzer, K. Zöllner, H.-J. Fuchs, E.-B. Kley, H. Zellmer, and A. Tünnermann, "High-power femtosecond Yb-doped fiber amplifier," Opt. Express 10, 628-638 (2002).
[PubMed]

A. Liem, J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, and A. Tünnermann, "High average power femtosecond fiber CPA system," in Advanced Solid-State Lasers, M.E.Fermann and L.R.Marshall, eds., Vol. 68 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 128-132.

Shore, B. W.

Strickland, D.

D. Strickland and G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56, 219-221 (1985).
[CrossRef]

Tennant, D. M.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

Tishchenko, A. V.

Tünnermann, A.

T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, and O. Parriaux, "An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings," Opt. Express 13, 10448-10456 (2005).
[CrossRef] [PubMed]

T. Clausnitzer, J. Limpert, K. Zöllner, H. Zellmer, H.-J. Fuchs, E.-B. Kley, A. Tünnermann, M. Jupé, and D. Ristau, "Highly-efficient transmission gratings in fused silica for chirped pulse amplification systems," Appl. Opt. 42, 6934-6938 (2003).
[CrossRef] [PubMed]

T. Clausnitzer, E.-B. Kley, H.-J. Fuchs, and A. Tünnermann, "Highly efficient polarization independent transmission gratings for pulse stretching and compression," in Optical Fabrication, Testing and Metrology, R. Geyl, D. Rimmer, and L. Wang, eds., Proc. SPIE 5252, 174-182 (2003).
[CrossRef]

J. Limpert, T. Schreiber, T. Clausnitzer, K. Zöllner, H.-J. Fuchs, E.-B. Kley, H. Zellmer, and A. Tünnermann, "High-power femtosecond Yb-doped fiber amplifier," Opt. Express 10, 628-638 (2002).
[PubMed]

A. Liem, J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, and A. Tünnermann, "High average power femtosecond fiber CPA system," in Advanced Solid-State Lasers, M.E.Fermann and L.R.Marshall, eds., Vol. 68 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 128-132.

Turunen, J.

J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P.Herzig ed. (Taylor & Francis, 1997), pp. 31-52.

Verdiell, J. M.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

White, A. E.

D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, "Production of in-fiber gratings using a diffractive optical element," Electron. Lett. 29, 566-568 (1993).
[CrossRef]

Yokomori, K.

Zellmer, H.

Zöllner, K.

Appl. Opt. (3)

Can. J. Phys. (1)

R. E. Collin, "Reflection and transmission at a slotted dielectric interface," Can. J. Phys. 34, 398-411 (1956).
[CrossRef]

Electron. Lett. (1)

D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, "Production of in-fiber gratings using a diffractive optical element," Electron. Lett. 29, 566-568 (1993).
[CrossRef]

J. Opt. A (2)

A. Drauschke, "Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization," J. Opt. A 8, 511-517 (2006).
[CrossRef]

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, "A transmission polarizing beam splitter grating," J. Opt. A 1, 215-219 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. B (1)

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J. M. Verdiell, "Characterization of near-field holography grating masks for optoelectronics fabricated by electron beam lithography," J. Vac. Sci. Technol. B 10, 2530-2535 (1992).
[CrossRef]

Opt. Acta (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
[CrossRef]

Opt. Commun. (1)

D. Strickland and G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56, 219-221 (1985).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Electron. 37, 309-330 (2005).
[CrossRef]

Proc. SPIE (1)

T. Clausnitzer, E.-B. Kley, H.-J. Fuchs, and A. Tünnermann, "Highly efficient polarization independent transmission gratings for pulse stretching and compression," in Optical Fabrication, Testing and Metrology, R. Geyl, D. Rimmer, and L. Wang, eds., Proc. SPIE 5252, 174-182 (2003).
[CrossRef]

Sov. Phys. JETP (1)

S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).

Other (2)

J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P.Herzig ed. (Taylor & Francis, 1997), pp. 31-52.

A. Liem, J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, and A. Tünnermann, "High average power femtosecond fiber CPA system," in Advanced Solid-State Lasers, M.E.Fermann and L.R.Marshall, eds., Vol. 68 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 128-132.

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Figures (10)

Fig. 1
Fig. 1

Setup (Littrow mounting) and relevant geometrical parameters.

Fig. 2
Fig. 2

Diffraction efficiency as a function of the fill factor and the groove depth for (left) TE and (right) TM polarization, and grating periods of (a), (b) 1000, (c), (d) 800, and (e), (f) 600   nm .

Fig. 3
Fig. 3

Electric fields of the TE modes (dashed curve, incident wave). (a) Mode 1 (propagating), (b) mode 2 (propagating).

Fig. 4
Fig. 4

F ( n e f f 2 ) for a fused silica grating with a period of 600   nm , a fill factor of 0.5 and TE polarization.

Fig. 5
Fig. 5

Section of F ( n e f f 2 ) from Fig. 4 for different fill factors. (a) TE polarization, (b) TM polarization.

Fig. 6
Fig. 6

Effective indices as a function of the fill factor for both polarizations.

Fig. 7
Fig. 7

Rigorous calculation of the diffraction efficiency of the negative first order as a function of the groove depth. (a) TE polarization (gray curve, two-mode model for f = 0.51), (b) TM polarization.

Fig. 8
Fig. 8

Illustration of the fill factor, where the two TM modes propagate with the same effective index, as a function of the period (wavelength 1.064   μm ).

Fig. 9
Fig. 9

Polarization contrast as a function of the groove depth and the fill factor. (a) Zeroth order, (b) negative first order (crosses, estimated parameters of the fabricated grating).

Fig. 10
Fig. 10

Polarization contrast of a grating with fill factor f = 0.519 , groove depth h = 1.365   μm as a function of (a) wavelength (angle of incidence 62.45°) and (b) incidence angle (wavelength 1.064   μm ). Arrows mark the possible tolerance for a contrast higher than 100:1 in both orders.

Equations (19)

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η 1 ( h ) = sin 2 ( π   h λ | n e f f 1 n e f f 2 | ) ,
cos α d = F ( n e f f 2 ) ,
F ( n e f f 2 ) = cos   β b cos   γ g β 2 + γ 2 2 βγ sin   β b sin   γ g ,
β = k 0 n b 2 n e f f 2 ,
γ = k 0 n g 2 n e f f 2 .
F ( n e f f 2 ) = cos   βb   cos   γg β 2 + ε b 2 γ 2 b βγ sin   β b sin   γ g ,
f = b / d = ( d g ) / d ,
1 = F ( n e f f 2 ) .
F ( n e f f 2 ) = cos   γ d .
n e f f 1 = n e f f 2 = cos φ i n ,
F ( n e f f 2 ) = cos   β d .
n e f f 1 = n e f f 2 = n cos φ ˜ i n .
h P = λ 2 n ^ e f f ,
Δ Θ = 2 π λ n ^ e f f h P = 2 π,
n ^ e f f = ε b 2 ε b ε b 2 1 .
β b + γ g = π
f ( d ) = π d γ β γ ,
h max T E = λ 2 | n e f f 1 T E n e f f 2 T E | .
C 0 = η 0 T M η 0 T E ,     C 1 = η 1 T E η 1 T M .

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